The Monty Hall problem is a famous probability puzzle based on a game show scenario. It’s named after Monty Hall, the original host of the television game show “Let’s Make a Deal.” Here’s how the problem is typically presented:
1. You are given the choice of three doors: Behind one door is a car; behind the others, goats.
2. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat.
3. He then says to you, “Do you want to switch to door No. 2?” Is it to your advantage to switch your choice?
**The Solution:**
– If you stick with your original choice, you have a 1 in 3 chance of winning the car.
– If you switch, however, the probabilities favor you. This is because if you initially picked a door with a goat (which happens 2 out of 3 times), switching doors will win you the car. Switching gives you a 2 in 3 chance of winning the car.
Here’s why switching is advantageous:
– Assume you always pick door 1.
– If the car is behind door 1 (1 out of 3 chances), the host can open door 2 or 3, and if you switch, you lose.
– If the car is behind door 2 (1 out of 3 chances), the host must open door 3, and if you switch, you win.
– If the car is behind door 3 (1 out of 3 chances), the host must open door 2, and if you switch, you win.
Thus, by switching, you win the car in two out of the three possible setups. The counterintuitive aspect of this solution, revealing the non-intuitive nature of probability, often surprises many people.
